As I consider myself to be an analyst first and foremost, I am interested in a wide range of analytical problems. However, within analysis I am most interested in Harmonic Analysis, Partial Differential Equations and Geometric Measure Theory and the connection between these areas.
More specifically, I am working on solving boundary value problems for linear elliptic and parabolic PDEs using Harmonic Analysis techniques and results from Geometric Measure Theory.
Dindoš, M., Pipher, J. & Ulmer, M. "The regularity problem for parabolic operators with transversally independent coefficients", Preprint, https://arxiv.org/abs/2509.06627
Ulmer, M. "Perturbation theory for the parabolic Regularity and Neumann problem", Preprint, https://arxiv.org/abs/2408.12529
Ulmer, M. "Equivalence between solvability of the Dirichlet and Regularity problem under an L^1 Carleson condition on \partial_t A", Preprint, https://arxiv.org/abs/2509.10328
Ulmer, M. "Solvability of the Dirichlet problem for a new class of elliptic operators", Preprint, https://arxiv.org/abs/2311.00614
Ulmer, M. "L^p boundary value problems for elliptic and parabolic operators", Ph.D. thesis, University of Edinburgh, United Kingdom, July 2024, http://dx.doi.org/10.7488/era/4636
Dindoš, M., Sätterqvist, E. & Ulmer, M. "Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part". Vietnam J. Math. 52, 519–566 (2024). https://doi.org/10.1007/s10013-023-00653-z